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皮特曼接近性度量：统计估计量的比较AI 解读

Preface Part I. Introduction 1. Evolution of Estimation Theory Least Squares Method of Moments Maximum Likelihood Uniformly Minimum Variance Unbiased Estimation Biased Estimation Bayes and Empirical Bayes Influence Functions and Resampling Techniques Future Directions 2. PMC Comes of Age PMC: A Product of Controversy PMC as an Intuitive Criterion 3. The Scope of the Book History, Motivation, and Controversy of PMC A Unified Development of PMC Part II. Development of Pitman's…

用于分类面板数据分析的条件对数线性模型AI 解读

Conditional log-linear models are developed for panel data and used to predict sequences of categorical responses. The class of models considered includes conventional Markov models and independence models as well as distance models in which all previous responses and present and past values of covariates are used to predict the current response. The approach taken in this article has some advantages over the marginal modeling approach that has become popular for…

作为回归局部方差解释度量的相关曲线AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

频率先验信念的经验评估：方法与先天性心脏病案例AI 解读

We consider the problem of critiquing prior beliefs concerning the distribution of a discrete random variable in the light of a sequentially obtained sample. A topical application concerns a probabilistic expert system for the diagnosis of congenital heart disease, which requires specification of a large number of conditional probabilities that are initially imprecisely estimated by a suitable “expert.” These prior beliefs may be formally updated as data become available,…

气象场时空统计建模方法：评论AI 解读

Abstract In this article we develop a random field model for the mean temperature over the region in the northern United States covering eastern Montana through the Dakotas and northern Nebraska up to the Canadian border. The readings are temperatures at the stations in the U.S. historical climatological network. The stochastic structure is modeled by a stationary spatial-temporal Gaussian random field. For this region, we find little evidence of temporal dependence while…

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卫星图像贝叶斯分类中的信息先验AI 解读

In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed…

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正则的回降秩估计AI 解读

A study is made of some unusual location estimates first proposed in 1977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established some strong robustness properties of these estimates, such as redescending influence functions and, in some cases, full efficiency at the Cauchy model. It is further shown here that the estimates, called M-W-S estimates, are derivable from a rank-based scheme founded on convex functions and hence are regular, are unique, and have…

定号二次型联合分布的近似AI 解读

Multidimensional Wilson-Hilferty transformations support Gaussian approximations to certain joint distributions of quadratic forms in jointly Gaussian variates. Central and noncentral joint distributions are studied and applications are noted. Parameters of the approximating distributions are given up to terms of order o(v −2) in the degrees of freedom v. Numerical studies validate using these approximations over a range of parameters for an essential subclass of the…

设计实验分析的预测方法AI 解读

Viewing the analysis of designed experiments as a model selection problem, we introduce the use of a predictive Bayesian criterion in this context based on the predictive density of a replicate experiment (PDRE). A calibration of the criterion is provided to assist in the model choice. The relationships of the proposed criterion to other prevalent criteria, such as AIC, BIC, and Mallows's C p , are given. An information theoretic criterion based on the PDRE's of two…

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使用狄利克雷过程先验估计正态均值AI 解读

In this article, the Dirichlet process prior is used to provide a nonparametric Bayesian estimate of a vector of normal means. In the past there have been computational difficulties with this model. This article solves the computational difficulties by developing a “Gibbs sampler” algorithm. The estimator developed in this article is then compared to parametric empirical Bayes estimators (PEB) and nonparametric empirical Bayes estimators (NPEB) in a Monte Carlo study. The…

近似贝叶斯推断AI 解读

Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties. This article proposes a measure of how close a system of interval estimates is to being of Bayesian form. Using this measure, several non-Bayesian…

平滑转换自回归模型的设定、估计与评价AI 解读

This article considers the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties…

回归图的解释AI 解读

A framework is developed for the interpretation of regression plots, including plots of the response against selected covariates, residual plots, added-variable plots, and detrended added-variable plots. It is shown that many of the common interpretations associated with these plots can be misleading. The framework also allows for the generalization of standard plots and the development of new plotting paradigms. A paradigm for graphical exploration of regression problems is…

线性模型中具有高崩溃点的秩估计AI 解读

An estimator in the linear model is defined by minimizing an objective function, the derivative of which is a signed rank statistic. The scores are generated from a function h+ : (0, 1) → [0, ∞), which is not necessarily nondecreasing, as is usually assumed. It is shown that this estimator can be chosen with a maximal breakdown point of. 5. Moreover, strong consistency and asymptotic normality (with convergence rate n −1/2 of the proposed estimator are proved under various…

切片逆回归中的维数确定AI 解读

A general regression problem is one in which a response variable can be expressed as some function of one or more different linear combinations of a set of explanatory variables as well as a random error term. Sliced inverse regression is a method for determining these linear combinations. In this article we address the problem of determining how many linear combinations are involved. Procedures based on conditional means and conditional covariance matrices, as well as a…

双重抽样中回归估计量的方差估计札记AI 解读

Double sampling of a finite population occurs when a sample from the population is itself sampled, with the intent of measuring varites in the subsample not already available in the sample. An important example is the regression estimator for means or totals, which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample. This article concerns estimation of the variance of the regression…

具有空间相关误差的回归模型AI 解读

In this article we consider regression models for two-dimensional spatial data when the errors follow a spatial unilateral first-order autoregressive moving average (ARMA) model studied by Basu and Reinsel. We give details on the convenient computation of the generalized least squares (GLS) estimator of the regression parameters in the presence of spatially correlated errors, and compare the GLS estimator to the ordinary least squares (OLS) estimator in some special cases.…